INTELLECT SHARPENERS All rights reserved.

Evening Post, Volume CXI, Issue 126, 30 May 1931, Page 6

INTELLECT SHARPENERS All rights reserved.

(By T. L. Briton.)

. QiinniHiinuiillliiiiniliHiiiiiiiiiiiiiiMiiiiiii •n«"«i«13 ,;"': Headers -with a little inj psnuity ■will find in this column an■ abun- ::. dant ■ store of entertainiuen k and « amusement, and the solving- 1 'of the : c;proWeins snould provide cxi wllent ': ■ mental exliilaration. , While • some ;- ol the "nuts" may appear t wrclei '*■" than' others-, it; will be ..found! that ii-none will require a sledge-hainmsr ;.7.,,t0 eractythem. ,-..-■ . ..;' ~<-:•"' .:. ..;(ByVT.-1. Briton.) '■•■■• ■M; ';■ POXES AND GEESE. [:'X':A correspondent has asked fiSrr the r: : jnt)libation of Sam Loyd's "Fqxijs and \ CrecsV"■ puzzlei'-fwhioli amused and othcr■tKvlse entertained' problem: love»'s. a, ■^enenitiorr ago. A square" sectkin of iVind has;n ;Sinall enclosure at ea<.ih of i&s jfour; .corners, ,A-,],Bi',C.;and D, a lane ruinning,-right round tho bound; tries lniide-giving acees's _from one to the i'tlier;■'■.,• Situated jii -'approximately, tho cenw'ife of the:section art! four more cnclosvires, E, IY'G, H,<but< these h»yo >. no direct road connectionwith each1 othtor. Fr.put' A there are two roads' pi' aceisss, one tv E/the other, direct to F, while from .\i a road le'ads'direct to H, wlii ph is closer to-B..thanto.any other corn or, just as F's nearest corner is A.-.Ahotlner road luads from enclosure .11. to fiUe south-eokstern corner C, the latter co. Un.ecting- also..'by:.road ■•- to G, which ;is : . situated-.r.iinmcdiatoly ..below.eiiclosui re 1T.....The .'.fourth:.corner; Dj has also tW'to road1 ebmtunnieations 'to the centre, on o to G and the other to E, thus makinj f; in additioiW-to the boundary-lanes ■eighilj' roads to tl»e centre enclosures from tkx.t| .corners,Ai fox is in each. o£ th.o..yftrdi"i I 1 and IS, ,i.|7hiio a. goose is located in^. each'of: the* enclosures Gr aiid'.H, and' the' problem 1 is to transfer the foxes to the gopse'.eiiHsicsui'fcs, and' .thegeese to, tfi'oi"'.foxes' -quarters in" 'the..;."fewest, number, of,, uioves, using any. of tho eight internal', roads,, or those along tho boundaries.- jQut ho enclosure ■ should j contain two aarihials at the same, time. WITH rOUE FICHJKES. - /.There;: are >oi«ly four examples" of a number.: containing jo,ur L . ...figures, all different, Ayhere two. of .them multiplied by the other. Wo\give a result consisting of the, same four, figures .employed. For instarico 'ZT Xtwiin'ty-seveh) multiplied ::15y- ■81-Ceightj'-o>^::' Vmakeia. .product consisting of the- same digits, not necessarily: in the same, order. And there-are only two*examples of a fourdigit number., m-wihich, tbtee of them multiplied by li'ic fourth give identically the same figures, in tho product. One of 'these .is-£73 (four, seven, three), multiplied."by" S (eight), equals 3784.. Ca'n\'ih«i reader find the other three examples in", the former case, and the only. qtlu:i\pne where the multiplier is only '"one!.'.figure, and the multiplicand thr^c?...But: in aJI cases the number must comprißo..£onr different digits. ' .:.-;.,. .- v;.v -• THBEE PIECES OF GOLD PLATE. Draw three circles of the respective sizes of a shilling, a sixpence, and athreepenny piece, these Uoins being { selected because their diameters would probably make, a right-ang,le triangle, . that of the shilling forming its hypotenuse, and the diameter of the threepenny-piece the perpendicular. If the sizes of thecoinH do'" nit exactly.--conform to tho making of v tbe,Jigure "•cometrically, let it be .i.tJtken. for: granted that they do, tho aug-jrtfs'tion touse them being prompted, by ifche feet that the equipment for this-problem is ready at hand. Three, solid plates of pure, gold are in the form described, and' ,the '"interesting /and.:.'-practical problem, is to.;cut them into the fewest number of pieces possiblo so. that they may "ho equally shared" between four' peoplej both in weight and superficial area. This is merely a question of practical geometry, and as the thickness of the plate is uniform, tho weight ■phase. .o.f the problem does not require aiiyrcflleulation,;.Tor ..t'lie,information of the would-be solver it may be staiod !i that the number of pieces into which ;tlie three plates may be cut in order .to theides'ifed result is fewer than i eight. ■■:-yv PARTNERS. ■Hbre as a little'question in evcry^ :..day''^nance which should interest the ■ ; ..read*er in so far that it may give him p a few moments of hard* thinking. Jones :j-'aria'-Brown are partners in a Stock Ex'.•change business, and when the profits i:.of last year were divided between them, - Jones received 5 per cent, on the •;• capital he had invested in the concern, ■ and Brown 4 per cent, on his. Both partners received equal amounts-in this ■' way, and the perplexing little question ■ arises, namely, how much did each of them receive as profits for the'year ■'. mentioned, if the joint capital invested '; was £22,500 (two, two, ftye,-nought, , jiougnt)l This little question came to •';» hand from "Student," who possibly met : the problem in an examination paper, ■ \ though, ho does not say so, the only ', comment made being that. he and his ;■ friends think that it has insufficient ';.- data. But perhaps the reader will join ]; issue with the young "gentlemen on that ■!, point. ' - • ' ' ' • ';; ' ELECTION. FiaUBES.r -■ f During the, progress .: of the - last i . municipal elections, figures oxhibited ' from time to !time during; the count ,';,; showed in sdvoral instances some re- :'■ ..markablc coincidences, obyio,us..to any ' observer -who looks for curiosities in ■figures. One board, showing the respec- ! : tive positions.'..of three ■ eaididates at the stage when 'each: had polled under ■ one thousand votes, but more'than one ; ■ hundred, revealed a mathematical sum !' in addition. The names were in alphabetical order, and the figures , against the name at the top, added to '■ ~ the number.polled by.candidate No. 2, ■ made a total which equalled .tho exact ': figures shown against th« nama -of the i -.' :third contestant. Here is a little arm- > chair problem arising from this • .coincidence. Supposing that "in-those ;.!nine figures no digit w.as repeated, and ~. 'that the total in. the bottom .row is ; ■; the smallest one-possible under these ;. conditions, dan the reader say what ' votes tho respective 'candidates had I ' polled at the stage when the board ■ ':'■' indicated such. position? .The-; cipher '-. may bo deemed a digit provided it be ; • given a place of arithmetical value.